We present a mathematical derivation of a discrete dynamical system by following a Fourier-Galerkin approximation of the 3-D incompressible magnetohydrodynamic (MHD) equations. In this way, a 6-D map, depending on 12 bifurcation parameters, is derived as a truncated set of nonlinear ordinary dierential equations (ODEs) to characterize incompressible plasma dynamical behaviors, also conserving total energy and cross-helicity in the ideal MHD approximation. Moreover, three dierent subspaces, associated with long-living non-trivial solutions (e.g., xed point solutions), have been found like the uid, magnetic, and the Alfvenic xed points. Our set can be seen as a Lorenz-like model to investigate MHD phenomena.
The poor man's magnetohydrodynamic (PMMHD) equations
Giuseppe ConsoliniMembro del Collaboration Group
;Vincenzo CarboneMembro del Collaboration Group
2020-01-01
Abstract
We present a mathematical derivation of a discrete dynamical system by following a Fourier-Galerkin approximation of the 3-D incompressible magnetohydrodynamic (MHD) equations. In this way, a 6-D map, depending on 12 bifurcation parameters, is derived as a truncated set of nonlinear ordinary dierential equations (ODEs) to characterize incompressible plasma dynamical behaviors, also conserving total energy and cross-helicity in the ideal MHD approximation. Moreover, three dierent subspaces, associated with long-living non-trivial solutions (e.g., xed point solutions), have been found like the uid, magnetic, and the Alfvenic xed points. Our set can be seen as a Lorenz-like model to investigate MHD phenomena.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
